We develop an analytic approach able to predict flow and bed topography in curved cohesionless wide channels. The novel feature of the present theory, compared with previous analytic approaches, is its ability to treat bottom perturbations of finite amplitude and situations such that sediment transport does not occur within the whole cross section. The theory is presently applied to the case of constant curvature channels though it can be extended, in principle, to channels with variable curvature. Results show that the dominant mechanism controlling the establishment of bed profile is the topographic feedback of bottom deformations on the flow field, while the role of the dispersive transverse transport of longitudinal momentum and of the metrically induced transverse variations of longitudinal slope is usually relatively small. The theory extends previous linear analyses which are shown to underpredict deeping of the cross section close to the outer bank. Also, unlike linear theories, the present approach predicts a transverse slope of the bed profile increasing towards the outer bend in agreement with experimental observations. The maximum depth is found to depend on the friction coefficient Cu of the undisturbed uniform stream and on the parameter &ngr;(&thgr;u)1/2/Cu where &ngr; is curvature ratio, that is, the ratio between channel half width and radius of curvature of the centerline, while &thgr;u is the Shields stress of the undisturbed uniform stream. Comparison with experimental observations is fairly satisfactory. The shape of the cross section is then determined also for values of &thgr;u close enough to the critical values not to allow bedload transport within the whole cross section. The threshold value of &thgr;u separating the total transport from the partial transport regime is finally determined as a function of the curvature ratio &ngr;. ¿ 1998 American Geophysical Union